Так модель очень простая, она легко программируется. А теперь прогоним ее по начальным числам от 10 то 1000
SP [11] motivation [1], iterations = [6] points [[11, 33, 66, 132, 264, 528, 1056]]
SP [12] motivation [1], iterations = [2] points [[12, 24, 48]]
SP [14] motivation [1], iterations = [4] points [[14, 84, 420, 840, 1680]]
SP [18] motivation [1], iterations = [4] points [[18, 36, 504, 3024, 6048]]
SP [24] motivation [1], iterations = [2] points [[24, 48, 96]]
SP [30] motivation [1], iterations = [8] points [[30, 60, 120, 240, 480, 6720, 13440, 591360, 1182720]]
SP [35] motivation [1], iterations = [8] points [[35, 105, 1785, 3570, 7140, 14280, 28560, 57120, 114240]]
SP [40] motivation [1], iterations = [2] points [[40, 80, 160]]
SP [42] motivation [1], iterations = [4] points [[42, 84, 420, 840, 1680]]
SP [44] motivation [1], iterations = [4] points [[44, 132, 264, 528, 1056]]
SP [66] motivation [1], iterations = [4] points [[66, 132, 264, 528, 1056]]
SP [78] motivation [1], iterations = [2] points [[78, 624, 1248]]
SP [84] motivation [1], iterations = [2] points [[84, 168, 336]]
SP [105] motivation [1], iterations = [4] points [[105, 210, 420, 840, 1680]]
SP [120] motivation [1], iterations = [6] points [[120, 240, 480, 6720, 13440, 591360, 1182720]]
SP [153] motivation [1], iterations = [4] points [[153, 306, 612, 1224, 2448]]
SP [210] motivation [1], iterations = [4] points [[210, 420, 840, 1680, 3360]]
SP [220] motivation [1], iterations = [4] points [[220, 1540, 6160, 123200, 246400]]
SP [231] motivation [1], iterations = [6] points [[231, 693, 3465, 353430, 706860, 1413720, 2827440]]
SP [264] motivation [1], iterations = [2] points [[264, 528, 1056]]
SP [420] motivation [1], iterations = [2] points [[420, 840, 1680]]
SP [435] motivation [1], iterations = [2] points [[435, 3480, 6960]]
SP [480] motivation [1], iterations = [4] points [[480, 6720, 13440, 591360, 1182720]]
SP [504] motivation [1], iterations = [2] points [[504, 3024, 6048]]
SP [510] motivation [1], iterations = [4] points [[510, 7140, 14280, 28560, 57120]]
SP [585] motivation [1], iterations = [4] points [[585, 1170, 14040, 421200, 842400]]
SP [612] motivation [1], iterations = [2] points [[612, 1224, 2448]]
SP [630] motivation [1], iterations = [4] points [[630, 1260, 2520, 5040, 10080]]
SP [642] motivation [1], iterations = [4] points [[642, 11556, 23112, 46224, 92448]]
SP [714] motivation [1], iterations = [4] points [[714, 14280, 28560, 57120, 114240]]
SP [776] motivation [1], iterations = [2] points [[776, 37248, 74496]]
SP [840] motivation [1], iterations = [2] points [[840, 1680, 3360]]
SP [903] motivation [1], iterations = [4] points [[903, 1806, 3612, 7224, 14448]]
SP [963] motivation [1], iterations = [6] points [[963, 2889, 5778, 11556, 23112, 46224, 92448]]
Сразу скажу, что я увидел первым делом, что далеко не все числа дают конечное количество движений. То есть большинство начальных чисел уходит в бесконечность. В тоже время, если небольшой набор чисел, которые дают конечное количество колебаний. Если посмотрите на них, то какие-то они очень знакомые. Пример графический, как если бы было движение вниз